Using a plane section to slice the square pyramid below would result in a square cross section. If Wich slicing direction were used.
If we slice the square pyramid from top to bottom (vertically), then it would result in a square cross-section. This is because the edges of the pyramid are perpendicular to the base, and if we slice it vertically, the cross-section would go through all four edges at equal distances from the apex, creating a square shape.
To determine the slicing direction that would result in a square cross-section of the square pyramid, we need to understand the symmetrical properties of the pyramid.
A square pyramid has a square base and four triangular faces that meet at a single apex or vertex. The symmetrical axis of the pyramid is a line connecting the apex and the center of the base.
To obtain a square cross-section, the slicing direction should be perpendicular to the symmetrical axis of the pyramid. This means the plane section should pass through the apex and cut the pyramid into two equal halves, with each half forming a triangular pyramid.
Since the symmetrical axis connects the apex to the center of the square base, slicing the pyramid vertically from the apex through the center of the base along the symmetrical axis will result in a square cross-section.